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A316264 FDH numbers of strict integer partitions with odd length and all odd parts. 0
2, 4, 7, 11, 16, 19, 25, 31, 41, 47, 53, 56, 61, 71, 79, 83, 88, 97, 101, 103, 107, 109, 113, 121, 127, 128, 131, 137, 139, 149, 151, 152, 154, 157, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199, 200, 211, 223, 224, 227, 229, 233, 239, 241, 248, 251, 257 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Let f(n) = A050376(n) be the n-th Fermi-Dirac prime. The FDH number of a strict integer partition (y_1,...,y_k) is f(y_1)*...*f(y_k).

LINKS

Table of n, a(n) for n=1..56.

EXAMPLE

Sequence of all strict odd integer partitions begins (1), (3), (5), (7), (9), (11), (13), (15), (17), (19), (21), (1,3,5), (23), (25), (27), (29), (1,3,7), (31).

MATHEMATICA

nn=100;

FDfactor[n_]:=If[n==1, {}, Sort[Join@@Cases[FactorInteger[n], {p_, k_}:>Power[p, Cases[Position[IntegerDigits[k, 2]//Reverse, 1], {m_}->2^(m-1)]]]]];

FDprimeList=Array[FDfactor, nn, 1, Union]; FDrules=MapIndexed[(#1->#2[[1]])&, FDprimeList];

Select[Range[nn], And[OddQ[Length[FDfactor[#]]], OddQ[Times@@(FDfactor[#]/.FDrules)]]&]

CROSSREFS

Cf. A000700, A050376, A064547, A213925, A258116, A279065, A299755, A299757, A305829, A316094.

Sequence in context: A261993 A299251 A238485 * A067744 A307601 A194215

Adjacent sequences:  A316261 A316262 A316263 * A316265 A316266 A316267

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jun 28 2018

STATUS

approved

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Last modified December 7 20:40 EST 2021. Contains 349589 sequences. (Running on oeis4.)